Electric power systems comprise power transmission networks interconnecting geographically separated regions, and substations for transforming voltages and for switching connections between individual lines of the network. Power generation and load flow in a system with several substations is managed by a central Energy Management System (EMS) and supervised by a Supervisory Control And Data Acquisition (SCADA) system. In the past years, continued load growth without a corresponding increase in transmission resources has resulted in an increased pressure to reduce operational security margins for many power systems world wide and to operate the power systems ever closer to their stability limits. These issues together with the on-going worldwide trend towards deregulation of the electric power markets in general have created a need for accurate and better network monitoring, protection and control.
In the past, only root mean square (RMS) values of voltages, currents, active power and reactive power flowing in the network have been determined in an unsynchronized way by means of conventional instrument transformers. Recently however, devices and systems for measuring voltage and current phasors at different locations of a network at exactly the same time have become available. Phasors are time-stamped, complex values such as amplitude and phase angle, of local electric quantities such as currents, voltages and load flows, and can be provided by means of Phasor Measurement Units (PMU) as presented e.g. in the article “PMUs—A new approach to power network monitoring”, ABB Review January 2001, p. 58. These units comprise a very accurate time reference, achievable e.g. by using Global Positioning Satellite (GPS) system and allowing synchronization of the time-stamped values from different locations. In an exemplary application for so-called wide-area monitoring, a number of PMUs forward their measured phasor values to a centrally located system monitoring centre. Data exchange can further be established between the system monitoring centre and other control and protection systems such as the SCADA system mentioned above, to allow for optimal data sharing and control actions.
An integral part of the aforementioned SCADA/EMS systems is the so-called State Estimation (SE) as described e.g. in chapters 1 and 2 (pages 1 to 33) of the textbook entitled “Power System State Estimation: Theory and Implementation” by A. Abur and A. G. Exposito (Marcel Dekker, New York 2004). SE involves a regular update of the most important quantities characterizing the power system, such as line flows, loads, generator outputs or bus voltages. Some of these quantities, e.g. transmission line flows, may not be observed directly, but can be derived from information about a topology and a number of states x of the power system. For example, these states x can be the magnitude and phase angle of bus voltages of all the buses of the power system. In short, the operating conditions or the static state of a power system at a given point in time can be determined if the network model and complex phasor voltages at every system bus are known.
As before the advent of phasor measurements, phase angles could not be measured due to lack of synchronization of measurement devices, SE was devised as a mathematical procedure for extracting the states x of the power system from a set of measurements z, such as voltage magnitudes V; line active P and reactive Q power flows. However, various types of additive errors and uncertainties v tend to influence these measurements.z=h(x)+v
Accordingly, the main feature of SE is a minimization of the impact of the errors v with help of redundant measurements. Typically, at a particular point in time, more measurements z are taken than the number of state variables to be determined. In this case, the above equation represents an over-determined set of nonlinear equations, for which a least-squares solution yields the vector x which minimizes the sum of the squares of the components of a residual vector. Generally, the situation is even more complicated since relationships between states and measurements are nonlinear, and the least squares solution of such a nonlinear estimation problem can only be obtained iteratively. Provided that there is enough redundancy in the measurement configuration, the existence of gross errors in the measurement set or structural errors in the network configuration can even be detected this way.
State estimation is based on the assumption that measurement errors are statistically distributed with zero mean. The major sources of such errors are a) the instrument transformers, b) the cables connecting the instrument transformers to the sensors and c) the sensors themselves. Furthermore, sub-optimal synchronization between different sensors introduces an additional uncertainty in the measurements.
The key ingredients to SE, apart from the measurements z mentioned above, are the network parameters and the actual network topology, comprising in particular updated information about every single component such as switches, breakers and transformers that are susceptible of changing a status. To this end, SE includes a topology processor that gathers status data about the circuit breakers and switches, and configures the one-line diagram of the system. Nevertheless, errors in the network topology and parameters do exist occasionally, due to unreported outages or transmission line sags on hot days.
Accordingly, the topology of the network needs to be updated automatically or manually depending on the switching status of the devices (line in or out e.g. for service or after a fault), and new network elements need to be added to the SE system after their installation in the power system. Likewise, potential problems with SE arise from those network parameters that are changing over time with ambient conditions (e.g. temperature, radiation) or from aging devices. Obviously, if the topology is not maintained carefully in the system, the SE results are inaccurate.
Generally, the SE assumes that the power system is in a steady-state situation. In transient situations, e.g. after a series of faults, the topology and the measurement values may appear to be incoherent, and the iterative procedure may be found to converge in an unsatisfactory way or not at all. Furthermore, in fringe areas of a power system, e.g. along remote transmission corridors, the redundancy of measurements is usually not given or weak, with such critical measurements resulting in an unobservable system if eliminated from the measurement set. Insufficient redundancy results in the SE procedure not being able to compensate either bad measurement values or inaccuracies in network parameters.
Among the abovementioned sources of errors or uncertainty, changes in parameters and topology may remain unnoticed by the state estimator. Nevertheless, no indicator or check has been proposed so far to determine if the state estimation procedure for a particular power system is basically correct or suffering from a serious bias due to an undiscovered change in parameter or topology.
Recently, Phasor Measurement Units (PMU) were proposed to serve as data sources for state estimation, e.g. for increasing the accuracy by adding additional redundant measurements. Obviously, if all the conventional sensors were replaced by PMUs, the angles of the voltages and currents of interest could be directly measured, and the update interval between subsequent sets of measurements reduced from several minutes to a fraction of a second. In this case, the subsequent SE procedure for deriving the most likely states x would be linear and thus decisively simplified:z=H·x+v, However, equipping all network nodes with PMUs for the sole purpose of SE is not realistic.